Pith. sign in

Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces

· 2021 · math.DG · arXiv 2112.01448

1 Pith paper cite this work. Polarity classification is still indexing.

1 Pith paper citing it
open full Pith review browse 1 citing papers arXiv PDF
abstract

In this paper we construct smooth Riemannian metrics on the sphere which admit smooth Zoll families of minimal hypersurfaces. This generalizes a theorem of Guillemin for the case of geodesics. The proof uses the Nash-Moser Inverse Function Theorem in the tame maps setting of Hamilton. This answers a question of Yau on perturbations of minimal hypersurfaces in positive Ricci curvature. We also consider the case of the projective space and characterize those metrics on the sphere with minimal equators.

fields

math.DG 1

years

2025 1

verdicts

CONDITIONAL 1

representative citing papers

The p-widths of $RP^2$

math.DG · 2025-01-23 · conditional · novelty 6.0

The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.

citing papers explorer

Showing 1 of 1 citing paper.

  • The p-widths of $RP^2$ math.DG · 2025-01-23 · conditional · none · ref 3 · internal anchor

    The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.